Common key cryptosystem wherein a cryptographic key being commonly used in both transmission and reception sides has been heretofore known. FIG. 8 is an explanatory view for explaining cryptographic processing in accordance with usual common key cryptograph. As shown in FIG. 8, the cryptographic equipment is composed of an extended key preparing means for preparing an extended key for cryptographic key, and a cryptographic processing means for encrypting a plaintext by the use of such extended key.
More specifically, since n-stages of cryptographic processing, i.e., cryptographic processing 1 to cryptographic processing n are implemented in the cryptographic processing equipment, extended key 1 to extended key n necessary for the n-stages of cryptographic processing are successively prepared in the extended key preparing means.
Accordingly, it is a very important problem in that a safe extended key is how rapidly prepared by the extended key preparing means in case of adopting common key cryptosystem.
In this connection, according to DES (Data Encryption Standard) cryptograph, extended keys 1 to n are prepared from a cryptographic key by means of only cyclical shifting and bit transposition, whereby a preparation of extended keys is realized at a high speed as shown in FIG. 9.
Furthermore, a process for preparing extended keys by means of MARS has been known as a process for preparing safer extended keys (a candidate cipher for AES, The First AES Conference, 1998, pages 1-9).
According to the above described DES cryptograph, however, an extended key is prepared by only cyclical shifting and bit transposition as shown by a mark  in FIG. 9, so that there are problems in view of safety. More specifically, even if information has been leaked as to one key among the number n of extended keys prepared by extended key preparing equipment, a cryptographic key itself to be input to extended key preparing equipment becomes clear in this DES cryptosystem, whereby problems of safety arise.
On the other hand, according to the above described MARS extended key preparing apparatus, information of a cryptographic key cannot be easily acquired from information of an extended key, so that there is no problem as to safety like in DES cryptosystem. However, another problem in such that many calculations must be repeated in the process, whereby the operations require much time arises.
From the matters described above, it has been a very important problem that a safe extended key required in case of applying common key cryptosystem is how rapidly prepared.